%I A075181
%S A075181 1,2,1,6,6,2,24,36,22,6,120,240,210,100,24,720,1800,2040,1350,548,120,
%T A075181 5040,15120,21000,17640,9744,3528,720,40320,141120,231840,235200,162456,
%U A075181 78792,26136,5040,362880,1451520,2751840,3265920,2693880,1614816
%N A075181 Coefficients of certain polynomials (rising powers).
%C A075181 This is the unsigned triangle A048594 with rows read backwards.
%C A075181 The row polynomials p(n,y) := sum(a(n,m)*y^m,m=0..n-1), n>=1, are obtained 
               from (ln(x)*(-x*ln(x))^n)*diff(1/ln(x),x$n), n>=1, after replacement 
               of ln(x) by y. Here diff(f(x),x$n) denotes n-fold differentiation 
               of f(x) with respect to x, n>=1.
%C A075181 The gcd of row n is A075182(n). Row sums give A007840(n), n>=1.
%C A075181 The columns give A000142 (factorials), A001286 (Lah), 2* A075183, 2*A075184, 
               4*A075185, 4!*A075186, 4!*A075187 for m=0..6.
%D A075181 Y.-Z. Huang, J. Lepowsky and L. Zhang, A logarithmic generalization of 
               tensor product theory for modules for a vertex operator algebra, 
               Internat. J. Math. 17 (2006), no. 8, 975--1012. see page 984 eq. 
               (3.9) MR2261644.
%D A075181 D. Lubell, Problem 10992, problems and solutions, Amer. Math. Monthly 
               110 (2003) p. 155. Solution 111 (2004) pp. 827-829.
%F A075181 a(n, m)= (n-m)!*|S1(n, n-m)|, n>=m+1>=1, else 0, with S1(n, m) := A008275(n, 
               m) (Stirling1).
%F A075181 a(n, m)=(n-m)*a(n-1, m)+(n-1)*a(n-1, m-1), if n>=m+1>=1, a(n, -1) := 
               0 and a(1, 0)=1, else 0.
%e A075181 1;2,1;6,6,2;24,36,22,6;...
%e A075181 n=2: (x^2*ln(x)^3)*diff(1/ln(x),x$2)=2+ln(x).
%o A075181 (PARI) {T(n, k)= if(k<0| k>=n, 0, (-1)^k* stirling(n, n-k)* (n-k)!)} 
               /* Michael Somos Apr 11 2007 */
%Y A075181 Cf. A048594, A075178, A007840, A075182.
%Y A075181 Sequence in context: A048999 A090582 A079641 this_sequence A052121 A117965 
               A111646
%Y A075181 Adjacent sequences: A075178 A075179 A075180 this_sequence A075182 A075183 
               A075184
%K A075181 nonn,easy,tabl
%O A075181 1,2
%A A075181 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 19, 
               2002